{"id":3200,"date":"2025-08-15T22:36:57","date_gmt":"2025-08-15T22:36:57","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=3200"},"modified":"2025-09-24T20:52:38","modified_gmt":"2025-09-24T20:52:38","slug":"sequences-and-their-notations-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/sequences-and-their-notations-apply-it\/","title":{"raw":"Sequences and Their Notations: Apply It","rendered":"Sequences and Their Notations: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Expand sequences defined by explicit and recursive formulas<\/li>\r\n \t<li>Write the explicit formula for a given sequence<\/li>\r\n<\/ul>\r\n<\/section>\r\n<div class=\"flex min-h-screen w-full overflow-x-clip\">\r\n<div class=\"h-screen w-full relative min-w-0\">\r\n<div class=\"flex flex-1 h-full w-full overflow-hidden relative\">\r\n<div class=\"max-md:absolute top-0 right-0 bottom-0 left-0 z-20 md:flex-grow-0 md:flex-shrink-0 md:basis-0 overflow-hidden h-screen max-md:flex-1\">\r\n<div class=\"flex flex-col h-full overflow-hidden\">\r\n<div class=\"flex-1 overflow-hidden h-full bg-bg-100\">\r\n<div class=\"relative h-full\">\r\n<div class=\"bg-bg-000 flex h-full flex-col relative\">\r\n<div class=\"ease-out duration-200 relative flex w-full flex-1 overflow-x-auto overflow-y-scroll\">\r\n<div class=\"w-full h-full relative\">\r\n<div class=\"w-full h-full relative [&amp;_*::selection]:bg-secondary-000\/10\" tabindex=\"0\">\r\n<div id=\"markdown-artifact\" class=\"font-claude-response mx-auto w-full max-w-3xl leading-[1.65rem] px-6 pt-4 md:pt-6 md:px-11\" tabindex=\"0\">\r\n<div>\r\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 !gap-3.5\">\r\n<p class=\"whitespace-normal break-words\">A small business is launching a new social media marketing campaign and needs to set realistic engagement goals and analyze their actual results. The marketing team creates a plan to steadily increase their weekly engagement. They model their engagement goals using the explicit formula:<\/p>\r\n<p class=\"whitespace-normal break-words\">[latex]a_n = 500 + 150n[\/latex]<\/p>\r\n<p class=\"whitespace-normal break-words\">where [latex]a_n[\/latex] represents their target engagement (likes, comments, shares) in week [latex]n[\/latex].<\/p>\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]312670[\/ohm_question]<\/section>\r\n<p class=\"whitespace-normal break-words\">After running the campaign for several weeks, the marketing team collects their actual engagement data.<\/p>\r\n\r\n<ul>\r\n \t<li class=\"whitespace-normal break-words\">Week 1: 800 engagements<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Week 2: 1,200 engagements<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Week 3: 1,800 engagements<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Week 4: 2,700 engagements<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Week 5: 4,050 engagements<\/li>\r\n<\/ul>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]312671[\/ohm_question]<\/section>\r\n<p class=\"whitespace-normal break-words\">The marketing team notices that their engagement growth is accelerating due to viral sharing effects. They predict that future weekly engagement will follow this pattern:<\/p>\r\n\r\n<ul class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-disc space-y-1.5 pl-7\">\r\n \t<li class=\"whitespace-normal break-words\">Start with 4,050 engagements (their week 5 result)<\/li>\r\n \t<li class=\"whitespace-normal break-words\">Each week, engagement will be 120% of the previous week plus an additional 300 engagements from new followers<\/li>\r\n<\/ul>\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]312672[\/ohm_question]<\/section><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Expand sequences defined by explicit and recursive formulas<\/li>\n<li>Write the explicit formula for a given sequence<\/li>\n<\/ul>\n<\/section>\n<div class=\"flex min-h-screen w-full overflow-x-clip\">\n<div class=\"h-screen w-full relative min-w-0\">\n<div class=\"flex flex-1 h-full w-full overflow-hidden relative\">\n<div class=\"max-md:absolute top-0 right-0 bottom-0 left-0 z-20 md:flex-grow-0 md:flex-shrink-0 md:basis-0 overflow-hidden h-screen max-md:flex-1\">\n<div class=\"flex flex-col h-full overflow-hidden\">\n<div class=\"flex-1 overflow-hidden h-full bg-bg-100\">\n<div class=\"relative h-full\">\n<div class=\"bg-bg-000 flex h-full flex-col relative\">\n<div class=\"ease-out duration-200 relative flex w-full flex-1 overflow-x-auto overflow-y-scroll\">\n<div class=\"w-full h-full relative\">\n<div class=\"w-full h-full relative [&amp;_*::selection]:bg-secondary-000\/10\" tabindex=\"0\">\n<div id=\"markdown-artifact\" class=\"font-claude-response mx-auto w-full max-w-3xl leading-[1.65rem] px-6 pt-4 md:pt-6 md:px-11\" tabindex=\"0\">\n<div>\n<div class=\"grid-cols-1 grid gap-2.5 [&amp;_&gt;_*]:min-w-0 !gap-3.5\">\n<p class=\"whitespace-normal break-words\">A small business is launching a new social media marketing campaign and needs to set realistic engagement goals and analyze their actual results. The marketing team creates a plan to steadily increase their weekly engagement. They model their engagement goals using the explicit formula:<\/p>\n<p class=\"whitespace-normal break-words\">[latex]a_n = 500 + 150n[\/latex]<\/p>\n<p class=\"whitespace-normal break-words\">where [latex]a_n[\/latex] represents their target engagement (likes, comments, shares) in week [latex]n[\/latex].<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm312670\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=312670&theme=lumen&iframe_resize_id=ohm312670&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p class=\"whitespace-normal break-words\">After running the campaign for several weeks, the marketing team collects their actual engagement data.<\/p>\n<ul>\n<li class=\"whitespace-normal break-words\">Week 1: 800 engagements<\/li>\n<li class=\"whitespace-normal break-words\">Week 2: 1,200 engagements<\/li>\n<li class=\"whitespace-normal break-words\">Week 3: 1,800 engagements<\/li>\n<li class=\"whitespace-normal break-words\">Week 4: 2,700 engagements<\/li>\n<li class=\"whitespace-normal break-words\">Week 5: 4,050 engagements<\/li>\n<\/ul>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm312671\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=312671&theme=lumen&iframe_resize_id=ohm312671&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p class=\"whitespace-normal break-words\">The marketing team notices that their engagement growth is accelerating due to viral sharing effects. They predict that future weekly engagement will follow this pattern:<\/p>\n<ul class=\"[&amp;:not(:last-child)_ul]:pb-1 [&amp;:not(:last-child)_ol]:pb-1 list-disc space-y-1.5 pl-7\">\n<li class=\"whitespace-normal break-words\">Start with 4,050 engagements (their week 5 result)<\/li>\n<li class=\"whitespace-normal break-words\">Each week, engagement will be 120% of the previous week plus an additional 300 engagements from new followers<\/li>\n<\/ul>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm312672\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=312672&theme=lumen&iframe_resize_id=ohm312672&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":67,"menu_order":6,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":156,"module-header":"apply_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3200"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":4,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3200\/revisions"}],"predecessor-version":[{"id":4354,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3200\/revisions\/4354"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/156"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/3200\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=3200"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=3200"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=3200"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=3200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}